A rocket, initially at rest on the ground, accelerates straight upward from rest with constant acceleration 58.8m/s^2 . The acceleration period lasts for time 8.00s until the fuel is exhausted. After that, the rocket is in free fall.

Find the maximum height y_max reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity equal to 9.8m/s^2

The general equations of accelerated motion also apply to falling (or rising) bodies with the exception that the term "a" for acceleration is replaced by the term "g” for the acceleration due to gravity). This results in